Compressing time-units in Markov Longitudinal Ordinal Models

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Hello everyone,

I’m currently working on a dataset where I need to handle recurrent events (multiple hospitalizations/heart attacks/revascularizations) and an absorbing state (death). My initial impulse was to just fit a cox model with a composite outcome, but on rethinking, I figured that this threw away quite a bit of data.

After reading up a bit (Prof. Harrell’s resources were excellent!), a Markov longitudinal ordinal model seemed ideal, and after fitting it, the gain in precision over the Cox with a simple composite was quite substantial.

I have 2 lingering questions:

  1. Time units: Although I have data on the day at which events occur, I’ve had practical difficulties using days as time-units because that makes the model-fitting process quite costly (computationally) since patients are often followed-up for a year or longer. I’ve tried to instead use weeks instead of days as time-units. I recognize this will lead to some loss in efficiency/precision (since there’ll be more ties in Y due to the coarser time-scale). Is there any practical guidance as to what extent it’s acceptable to compress time-scales for computational purposes? Most of the examples I’ve seen assessed relatively short-term (~ 1 month) scales.

  2. Event durations (or lack thereof): For one event type in particular (hospitalization), I only have data on the date at which hospitalization occurred but not for how long it lasted. I recognize this will inevitably lose me some precision (since some patients will experience longer hospitalization), but would it be defensible to model hospitalizations as a one-time-event (similar to an MI or a revascularization procedure) in the absence of information on hospitalization duration?

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Hospitalized as one time event defensible but you will need to define your “average hospital length of stay” during which an individual who has experienced the hospitalization event is not at risk for a hospitalization, because presumably a currently admitted patient is not at risk of being admitted

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I would analyze the data weekly. Another option is once you are finished, repeat the analyses once more using daily status and take that as the final product. Or compare the two to see if anything changed.

You really, really need the end dates of hospitalization to be able to get state occupancy probabilities. And even transition probabilities can be messed up without having access to the needed data, e.g., you will find a high probability of transitioning from a hospitalized state to being at home and that probability will be biased.

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Thanks a lot Elias! Fortunately there’s a bit of literature on the average length of hospitalization I’m interested in (HF hospitalization). It’s approximately 1 week which I guess is a bit of a happy coincidence in that’s the smallest time-unit I would have.

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Thanks a lot Prof. Harrell. Would the upwardly-biased probability of transitioning from hospital to home still apply if the average length of hospitalization is ~1 week (which is also the smallest time-unit I have)?

I imagine there’s probability a of loss of efficiency if the marker predicts a shorter duration of hospitalization or if it reduces the proportion of people who significantly overstay. But I wouldn’t expect the state-occupancy probabilities to be systematically over/under-estimated in this scenario (unless my intuition betrays me).

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This prevents you from doing analyses with 1-day resolution but weekly resolution analysis will be OK if say 60% of the hospitalizations are between 6 and 8 days long.

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Got it, that makes sense. Thanks a lot!